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This work shows that the logical space of any non-trivial fermionic error-correcting code contains no pure fermionic Gaussian state, utilizing a fundamental incompatibility between fermionic error correction and Wick's theorem.
It is proved that a resource-constrained learner cannot gain any advantage through classical interaction with an untrusted prover, and it is shown that for the vast majority of testing and learning problems, a memory-constrained quantum algorithm cannot overcome its limitations via classical communication with a memory...
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